Is there a way to make the grid bigger in the U.V. screen?
You can have any number of UVs for a single mesh. In the object data tab of the Properties panel you'll find the UV Maps section. Select the verts of your model where you want texture1 to go and hit U-->Unwrap. That will create the first UV Map. Now hit the "+" button next to the window and select the verts where you want texture2 to go and hit U-->Unwrap. That will create UVMap.001. By control/clicking on the names you can change them (for example, "UVMap.001" to "Texture2" so it's easy to find later). You can do this many times but there is a limit (not sure what it is but high enough for most needs). Finally in the node editor Add-->Input-->UVMap, select map and plug into vector slot on your texture node. Repeat for all textures.